The use of mathematical models has been fundamental to understanding all aspects of fluid dynamics, not-least those problems relating to the flow of fluid through arteries. Of particular interest for the present work is the first analytical expression for the velocity of a viscous incompressible fluid through an axisymmetric pipe, derived by [1]}. In this study we will utilise the perturbation techniques of [2]} to consider the asymptotic correction terms to the Womersley flow profile due to a microvascular anastomosis, simplifying the problem by noting that we can consider sections of vessel which have a radial length scale that is much smaller than the axial length scale. The use of such simplifications, as well as other mathematical techniques, have been widely used to great success for related problems in blood flow; for a detailed explanation of the subject see [3]}. These techniques will enable significant analytical progress to be made in understanding the changes in shear rate across the site of anastomosis, and thus will bring new insight into the ways in which rates of thrombosis may be further reduced.
